I need a ticket rule that re-opens a ticket when the submitter responds after it has been closed

At the moment, when the submitter of a closed ticket replies to that ticket, it does not re-open the ticket, nor alert the owner. This means comments following ticket closure are missed. Is there a rule that can be created to make the closed ticket re-open and alert the owner once a comment is made but not the user satisfaction survey?

- Enter message (mine says: Closed ticket $ticknum owned by "$owner_name" has been reopened. You may review the ticket here: http://kbox/adminui/ticket$id=$ticknum. The status was "$$status_name" and is now marked as "Reopened".)